Group with Order Less than 60 is Solvable

Theorem

Every group whose order is less than $60$ is solvable.

Proof

A direct consequence of Burnside's Theorem: the smallest number with $3$ distinct prime factors is $2 \times 3 \times 5 = 60$.

The validity of the material on this page is questionable. In particular: But $2 \times 3 \times 5 = 30$ not $60$. See talk page. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by resolving the issues. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Questionable}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

$\blacksquare$

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Normal and Composition Series: $\S 75 \gamma$